Question

A survey of all students at a large high school revealed that, in the last month, 38% of them had dined at Taco Bell, 16% had

dined at Chipotle, and 9% had dined at both. Suppose we select a student at random.
What's the probability that the student has dined at Taco Bell or Chipotle in the last month?
Round your answer to 2 decimal places.
Leave your answer in decimal form.

Answer 1

The probability that a randomly selected student has dined at Taco Bell or Chipotle in the last month is 0.45 or 45% after applying the inclusion-exclusion principle.

Step-by-step explanation:

The probability that a selected student has dined at either Taco Bell or Chipotle can be found using the principle of inclusion-exclusion. The principle is to add the individual probabilities and subtract the probability of the intersection to avoid counting those students twice. The probability of having dined at Taco Bell is 38% (0.38) and at Chipotle is 16% (0.16). The probability of having dined at both is 9% (0.09).

To calculate the probability that a student has dined at Taco Bell or Chipotle (or both), the formula is P(Taco Bell or Chipotle) = P(Taco Bell) + P(Chipotle) - P(Both). Plugging in the numbers: P(Taco Bell or Chipotle) = 0.38 + 0.16 - 0.09 = 0.45 or 45% when converted to a percentage and rounded to two decimal places.

So, the probability that a randomly selected student has dined at Taco Bell or Chipotle in the last month is 0.45 or 45%.